Access from internet (and localhost) to xampp admin page (by server's IP), phpmyadmin (through xampp page) and hosted website (domen through vhost) are ok, but webalizer blinks with info that log was created, and gives 404 after it. 404 on page http://my.ip.is.here/webalizer/ and "Please inform the author of that page about the error." with link to http://my.ip.is.here/webalizer.php . Security all are "SECURE", in Status - MySQL database, PHP, Perl, Common Gateway Interface (CGI), Server Side Includes (SSI) are "ACTIVATED".

Check the ownership of the generated files in /opt/lampp/htdocs/webalizer. I'm betting they are owned by root:root, and that is likely the source (just a hunch) While you are at it, it would be good to check the permissions as well - probably 'should be' 644.